This paper seeks to unconventionally maximize the volatility of a portfolio through a quartic optimization based on Markowitz’s modern portfolio theory, which generally seeks to do exactly the opposite. It shows that through this method, a daily leveraged exchange traded fund (ETF) strategy investigated by Posterro can be significantly improved upon in terms of its Sharpe ratio. The original strategy seeks to use a combination of momentum trading and tracking error in leveraged ETFs to trade during the last half an hour of the trading day, but it suffers in a low volatility market. By maximizing the volatility to take better advantage of tracking error and momentum, this problem is addressed by both increasing the mean daily return and significantly decreasing the variance of the strategy’s daily returns. GARCH forecasting is also implemented to assist in the maximization of the daily portfolios’ variances, though this does not prove to make a statistically significant difference in the strategy’s performance.

Recently, there are more and more literatures discuss on the issues of investment strategies of leveraged ETFs. In our works, we concentrate our issues on optimal leverage of ETF of S&P 500 index. Based on ARMA-GARCH model¡¦s assumption, we find out that the forecasting optimal leverage can be shown in a formula which contains return and characteristic function. In this paper, we use MA(1)-GARCH(1,1) to forecast volatility based on 1008 rolling window to forecast one day ahead¡¦s volatility; and our estimation time is start from 1954 to March 2011. In this paper, we present four dynamic leverage models (Normal, Student T, VG, and Best model¡¦s leverage) to find out the payoffs under these models. In our model, the forecasting accuracy is just about 55% which is slightly higher than SPX raise probability. But during long-term compound effect, the dynamic leverage models can out-perform than constant leverage. There may exist some important factors in these results, one of them is the crash forecasting ability. During 1980 to 2011 SPX has 14 big crashes and these models can effectively avoid 10 big crashes. In short-term investment horizon none of these five models are always outperform than others but in long-term investment horizon the strategy of best model¡¦s leverage can always earn money when investment horizon is 2400 days.